How to prove that f = xsinx is not a uniform continuous function on R? That is to say, it is proved that X and Y belong to R. when x approaches y, f (x) does not approach f (y) Could you give me a hint how to prove it?

The uniformly continuous function is: as long as the independent variable | x1-x2 | ξ
Therefore, f = xsinx is not a uniformly continuous function on R

RELATED INFORMATIONS

1. Excuse me: judge the number of zeros of function f (x) = xsinx-3 / 2 in (0, π) and prove it thank you.
2. If f (x + 2) - f (x) = 1 holds, is f (x) a periodic function?
3. Given the function f (x) = 1 / (1 + x ^ 2), then f (2013) + F (2012) + F (2011) + +f(2)+f(1)+f(1/2)+…… The value of F (1 / 2011) + F (1 / 2012) + F (1 / 2013) is
4. Given the function f (x) = X21 + X2, then f (12013) + F (12012) + F (12011) + +f(12)+f(1)+f（2）+f（3）+… +f= ___ ．
5. Function f (x) = (1 + x-x22 + x33-x44 + -The number of zeros of cos2x on interval [- 3, 3] is () A. 3B. 4C. 5D. 6
6. It is known that the function f (x) is an even function on R, satisfying f (x) = - f (x + 1). When x ∈ [20112012], f (x) = x-2013, then () A. f(sinπ3)＞f(cosπ3)B. f（sin2）＞f（cos2）C. f(sinπ5)＜f(cosπ5)D. f（sin1）＜f（cos1）
7. Let f (x) be an odd function with a period of 3 and f (- 1) = 1, then f (2008) =?
8. It is known that the function f (x) defined on R with the minimum positive period of 5 satisfies f (- x) = - f (x), And f (3) = 0, then in the interval (0,10), the number of solutions of the equation f (x) = 0 is?
9. Finding the maximum and minimum of trigonometric function in high school mathematics (p90,27) Y = SiNx - radical (3) cosx, X ∈ R; According to the difference angle formula of trigonometric function, 2Sin (x - π / 3) = SiNx - radical (3) cosx can be obtained Yin-1
10. Given the function FX = SiNx + cosx, X belongs to [- open / 2, Wu / 2] to find the maximum and minimum value of FX
11. The quadratic function f [x] = x ^ 2 + X + a [A. > 0] is known if f [M]
12. Let f (x) = x & # 178; - x + a (a > 0), if f (m)
13. Quadratic function f (x) = x & # 178; - x + A, if f (- M)
14. One kW. H electric energy can supply the normal working time of the fluorescent lamp marked with 220 V and 40 W
15. F. How to read MF, UF, NF, PF in Chinese? And their conversion?
16. What is the voltage measured after the ammeter G is series connected with a resistor and refitted into a voltmeter? Is it the voltage of the optical ammeter g or the voltage of the ammeter with that resistor?
17. Two fixed value resistors R1 and R2 are connected in series to the power supply, and the total power is P1. They are connected in parallel to the original power supply, and the total power is P2. Assuming that the output voltage of the power supply does not change, then () A. P1 ＞ P2 B. P1 ＜ P2 C. P1 = P2 D. cannot be determined Is there an easier way to copy? Please don't wait online,
18. A bulb is marked with pz220 100. In order to make the bulb work normally after being connected to the 330V circuit, what is the resistance in series or in parallel?
19. The price of type a refrigerator sold in shopping malls is 2190 yuan per unit, and the daily power consumption is 1 degree, while the price of type B energy-saving refrigerator is 10% higher than that of type a refrigerator, but the daily power consumption is 0.55 degree? (calculated according to the service life of 10 years, 365 days per year and 0.40 yuan per kilowatt hour)
20. What is the resistance symbol There is a frame in the middle. There is a horizontal line at the top and a horizontal line at the bottom, In the middle of a box, there is a horizontal line at the top of the left corner, and there is also a horizontal line at the bottom of the right corner. A diagonal line in the middle connects two horizontal lines. If you can explain it in detail, the more the better, there will be extra points